Laser apparatuses such as these are known, for example, from the document DE 100 26 734.3. This application claims the priority of the German patent application DE 102 43 545.6 dated Sep. 19, 2002. The content of the documents DE 100 26 734.3 and DE 102 43 545.6 is herewith incorporated by reference into the present description. These documents describe an optically pumped quantum well structure which is arranged together with a pump radiation source, for example a pump laser, on a common substrate. The quantum well structure and the pump radiation source have different radiation-emitting layers, which are designed such that the wavelength of the which is emitted from the pump radiation source is shorter than the wavelength of the radiation which is produced by the quantum well structure. This wavelength difference is necessary since, otherwise, if the pump wavelength and the emission wavelength were the same, the radiation produced by the quantum well structure would be absorbed in the quantum well structure in the same way as the pump radiation and, in consequence, the efficiency of the laser apparatus would be greatly reduced. In the case of a vertically emitting laser formed by the quantum well structure, this would in particular prevent the stimulation of oscillations of the vertically emitting laser.
A semiconductor laser apparatus of that kind may, for example, be grown in successive epitaxial steps on an epitaxial substrate. In this case, the quantum well structure is initially grown over the entire area, after which a subarea of it is removed, and the pump radiation source is grown on the area of the epitaxial substrate exposed in this way. Since each epitaxy step increases both the production duration and also the costs incurred by it, production with as few epitaxy steps as possible is desirable.